The mesh picture does not show shared mesh at the body interfaces. You should be able to use contacts instead of shared mesh if you don't want to share the mesh. If the geometry comes from SpaceClaim, use "Workbench [ribbon] > Share." Since you have some thin bodies, make sure the tolerance in the Options panel is less than the thickness of the thin bodies:
If the geometry comes from DesignModeler, shift-select all the bodies, then right click to "Form New Part."
Additionally, you won't be able to run the electric (and thermal?) analysis with no voltage assigned. You will need a reference voltage assigned somewhere in the model, even if it is all connected correctly.
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